If the metric is asymptotically flat, it is straightforward to assign meaning to a quantity, such that it resembles the energy we know from special relativity. In particular, for the Kerr metric we may regard $(\partial_t)^a$ as a vector representing the stationary observer at infinity, where space-time is Minkowski, and the rest appears to said observer as an isolated system. If the definition of a scalar is such that it matches the energy in the asymptotic region, say $-p_a(\partial_t)^a$ with $p^a$ the momentum of a test particle, then we may regard it as energy forin the entire space-time.

If the metric is asymptotically flat, it is straightforward to assign meaning to a quantity, such that it resembles the energy we know from special relativity. In particular, for the Kerr metric we may regard $(\partial_t)^a$ as a vector representing the stationary observer at infinity, where space-time is Minkowski, and the rest appears to said observer as an isolated system. If the definition of a scalar is such that it matches the energy in the asymptotic region, say $-p_a(\partial_t)^a$ with $p^a$ the momentum of a test particle, then we may regard it as energy for the entire space-time.

If the metric is asymptotically flat, it is straightforward to assign meaning to a quantity, such that it resembles the energy we know from special relativity. In particular, for the Kerr metric we may regard $(\partial_t)^a$ as a vector representing the stationary observer at infinity, where space-time is Minkowski, and the rest appears to said observer as an isolated system. If the definition of a scalar is such that it matches the energy in the asymptotic region, say $-p_a(\partial_t)^a$ with $p^a$ the momentum of a test particle, then we may regard it as energy in the entire space-time.

If the metric is asymptotically flat, it is straightforward to assign meaning to a quantity, such that it resembles the energy we know from special relativity. In particular, for the Kerr metric we may regard $(\partial_t)^a$ as a vector representing the stationary observer at infinity, where space-time is Minkowski, and the rest appears to said observer as an isolated system. If the definition of a scalar is such that it matches the energy in the asymptotic region, say $-p_a(\partial_t)^a$ with $p^a$ the momentum of a test particle, then we may regard it as energy for the entire space-time.